Second order optimal approximation in a particular exponential family under asymmetric LINEX loss

In this paper, we consider the problem of sequentially estimating the unknown parameter in a particular exponential family of distributions under an asymmetric LINEX loss function and fixed cost for each observation within a Bayesian framework. Under a gamma prior distribution, the second order approximation for the Bayes risks of the asymptotically pointwise optimal rule and the optimal stopping rule are derived. It is shown that the asymptotically pointwise optimal rule is asymptotically non-deficient in the sense of Woodroofe (1981).